Question

The letters if the word MISSI SSIPI are arranged in a row at random. Then the probability that all S's come together is ?


Problem on Classical Probability.

Answer 1

Hey there mate the spelling is MISSISSIPPI

What is the probability that 4 Ss appear consecutively in the word Mississippi assuming that the letters are arranged at random?
The word “mississippi” consists of m(1),i(4),s(4),p(2)

###the numbers in bracket are cardinality###

So total permutations=11!/(4!*4!*2!)=34650

If 4s appear consecutively ie appear together, then 4s can be denoted by a character say X.

So we've now 8 characters i.e m(1),i(4),X(1),p(2)

Again total permutations=8!/(4!*2!)=840

So favourable cases are 840

hence probability = 840/34650=4/165

Answer 2

Given word is MISSI SSIPI.

= > It has 10 letters, 4 S's, 4 I's.

= > 10!/4!4!

(1)

Consider All the 4'S as 1 unit and the other 6 letters - 4 I's, 1 M, 1 P.

Total number of combinations in which 4's come together = 7!/4!.

Now,

Required probability = (7!/4!) * (4!4!/10!)

= > 5040/151200

= > 1/30.

Hope this helps!